As an addition to the above - it appears that better translations have surfaced along with more information.

Here is a link to a game walkthrough. It is in japanese, but a google chrome translation is fairly well and should help your through the game. It lists victory conditions of each battle. The last chapter lists the battles required to recruit the special characters.

This game is not region free and will require a japanese xbox to play. That is, unfortunately, the only thing stopping me from playing it (as well as the other 5 or so SRPGs that weren't brought state-side).

Character Ranking (100)
A character has reached level 100.(I would assume this is as easy as leveling one of your party members to level 100. I do not know whether this will occur with regular play or if you'll need to grind post-story.)

Do 10,000 Damage (100)
Unleash a 10,000 damage combo.(Deal 10,000 damage during a single combo. A post over at TA makes this seem fairly easy - he found a enemy weaker than his party by 8 levels and had his entire team involved in a combo from behind.)

Entire Enemy Defeat (100)
Number of enemies defeated exceeds 1,000.(Defeat 1,000 total enemies. I do not know whether this will occur with regular play or if you'll need to grind post-story.)

Random Map Clearing (100)
Cleared 100 random maps.(Complete 100 different random battles. I do not know whether this will occur with regular play or if you'll need to grind post-story. I also don't know if story-required battles count or if they must be random battles.)

Skill I (50)
Learned Hyakki Night(I believe all of the skill-related achievements are obtained by having a specific character obtain a specific skill. The skills, as far as I can tell, are earned by leveling up - so it's just a matter of leveling the specific characters.)

Skill II (50)
Byrne learned Space(I believe all of the skill-related achievements are obtained by having a specific character obtain a specific skill. The skills, as far as I can tell, are earned by leveling up - so it's just a matter of leveling the specific characters.)

Skill III (50)
Learned H.G.M.M.(I believe all of the skill-related achievements are obtained by having a specific character obtain a specific skill. The skills, as far as I can tell, are earned by leveling up - so it's just a matter of leveling the specific characters.)

Skill IV (50)
Tian Fengshan learned Destroy(I believe all of the skill-related achievements are obtained by having a specific character obtain a specific skill. The skills, as far as I can tell, are earned by leveling up - so it's just a matter of leveling the specific characters.)

Skill V (50)
Learned Rikidaiza(I believe all of the skill-related achievements are obtained by having a specific character obtain a specific skill. The skills, as far as I can tell, are earned by leveling up - so it's just a matter of leveling the specific characters.)

Skill VI (50)
Arrow learned God(I believe all of the skill-related achievements are obtained by having a specific character obtain a specific skill. The skills, as far as I can tell, are earned by leveling up - so it's just a matter of leveling the specific characters.)

Special Character 1 Joined (100)
Juju joined the party(It appears that all three special characters can join on playthrough one at the end of the game. Different missions are required for each.)

Special Character 2 Joined (100)
Gaza joined the party(It appears that all three special characters can join on playthrough one at the end of the game. Different missions are required for each.)

Special Character 3 Joined (100)
Reguraito joined the party(It appears that all three special characters can join on playthrough one at the end of the game. Different missions are required for each.)